Bathymetric Influences on the Estuarine Equilibrium Length and Adjustment Time

Linear theories are extended to enable investigations of how exponentially convergent width and sloping bottom affect the sensitivity of estuarine equilibrium length and adjustment time. This study focuses on the response to river forcing and considers a regime dominated by gravitational circulation, but the results are generalizable. For a range of forcing and bathymetric profiles, the predicted equilibrium length and adjustment time compare favorably with numerical solutions from a width-averaged model. The main findings are that 1) convergent width and sloping bottom reduce the sensitivity of equilibrium length to river forcing. The sensitivity is governed by a dimensionless parameter that measures the degree of width and depth changes sampled by the intrusion length. Hence, the sensitivity is not a constant in a system but varies with forcing: when discharge increases, a shortened estuary experiences less bathymetric changes over its intrusion. The sensitivity therefore increases progressively toward the conventional −⅓ power law. An observational example of variable sensitivity from Delaware Bay is given. 2) Width convergence and bottom slope help accelerate the adjustment process. It is shown that the linear adjustment time is set by the ratio of salt content variations to the discharge perturbation. Hence, under the same forcing, the adjustment time is controlled by the salt content variations, which decrease monotonically with increasing convergence and slope. This means that, to achieve a given length change, a more strongly convergent and sloped system simply requires transport of less salt, thereby needing a shorter adjustment time.